Regularized variational principles for the perturbed Kepler problem
| Autor: | Vivina Barutello, Gianmaria Verzini, Rafael Ortega |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Change of variables General Mathematics Dynamical Systems (math.DS) 01 natural sciences Regularization (mathematics) Kepler symbols.namesake Mathematics - Analysis of PDEs Kepler problem 0103 physical sciences Classical Analysis and ODEs (math.CA) FOS: Mathematics Order (group theory) 0101 mathematics Mathematics - Dynamical Systems Mathematics Dirichlet problem 010102 general mathematics Action (physics) Mathematics - Classical Analysis and ODEs symbols 010307 mathematical physics Symmetry (geometry) Analysis of PDEs (math.AP) |
| Popis: | The goal of the paper is to develop a method that will combine the use of variational techniques with regularization methods in order to study existence and multiplicity results for the periodic and the Dirichlet problem associated to the perturbed Kepler system \[ \ddot x = -\frac{x}{|x|^3} + p(t), \quad x \in \mathbb{R}^d, \] where $d\geq 1$, and $p:\mathbb{R}\to\mathbb{R}^d$ is smooth and $T$-periodic, $T>0$. The existence of critical points for the action functional associated to the problem is proved via a non-local change of variables inspired by Levi-Civita and Kustaanheimo-Stiefel techniques. As an application we will prove that the perturbed Kepler problem has infinitely many generalized $T$-periodic solutions for $d=2$ and $d=3$, without any symmetry assumptions on $p$. 49 pages, 2 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|